Is the case stainless steel or silver toned plastic or resin?

It's definitely all stainless steel. Get one. Cool watch.

How can i adjust the watch bracelet to make it longer

Under the the main clasp there in the middle there is a rectangular gap, it is very stiff, but you have to take a small Jeweler screwdriver, (wrap the tip of screwdriver, so you do not scratch watch bracelet) and place in the rectangular slot and leverage up. It will ‘pop’ up and then you can slide the clasp, push down when you find correct length. I also used a shot of WD 40 in the slot area before lifting clasp up. This helped loosen it.

how does this watch compare to the much cheaper Casio retro watches ?

Great watch, worth the price, get either of the stainless steel, with blue LED or the Green LED if you can. Accurate, retro, clear great conversation starter. Compared to Casio bracket the same or better. The case is all steel much better than Casio case which in some instances is a resin plastic. Numerals a good size. The cheaper Casio with similar style are LCD with light or screen that is illuminated. The Amitron the LED’s light up on a dark background.